It’s a strange thing for a mathematical person to say, but some people are luckier than others. Luckily for our son (or his parents), we shop at Countdown, which means he received a regular supply of Disney-Pixar Domino Stars throughout the 6.5 week promotion.

It was all a bit of a yawn to me, this time round. Having calculated the chances of collecting a full set of Dreamworks Heroes Action Cards, I was neither surprised nor frustrated by the increasing number of duplicates as his collection grew. The theoretical hyperbolic growth of the number of packets he would have to open to find a new domino implied a spend of $4480 to complete a set of 50. Almost $700 per week?? Not very likely.

To cut a long story short, on the last day of the promotion, we trudged home from a swap meet needing just two more to complete the set. Our chances of finding those last two looked bleak…except that a neighbour had just dropped off a big bag of 22 packets in our letterbox.

As I said, some people are luckier than others, and to our amazement, our son actually found the very two that he needed! Now how lucky is that?! I mean, what are the chances…?

Without going into too much detail, you can either focus on what you don’t want to happen, i.e. you get none of one of the coveted dominoes and any number of the other:

or you can focus on what you do want to happen, i.e. you eventually find one of the two that you’re looking for, and then hope to find the other one amongst the packets remaining:

But a friend of ours came up with an expression that best reflects what really happened, i.e. our son stopped opening packets as soon as he found the two he needed:

Reassuringly, all three expressions evaluate to this rather impressive looking fraction:

So it was very close to a 1 in 8 chance. Our son doesn’t realise just how lucky he is.

Over the past two weeks, there has been a flurry of public discussion about primary maths education in New Zealand. Two reports, released within a week of each other, came out with the same message: our primary school children are performing very badly in maths. Not exactly news, but it’s good to see the nation talking about it.

Releasing the Crown’s National Monitoring Study of Student Assessment on Mathematics and Statistics (2013?!) late on a Friday before the long Queen’s Birthday weekend was a possible reason for the muted response to the latest depressing statistic: only around 41% of approximately 2000 Year 8 students in 2013 met the expected level of achievement. Our primary school leavers are struggling with decimals, fractions and percentages, and don’t I know it…

But what really got people riled up was The New Zealand Initiative’s report, “Un(ac)countable: Why millions on maths returned little”, written by Rose Patterson. As the Minister of Education said herself, it provided a “fresh perspective” on New Zealand’s maths learning woes.

Now that the media hullabaloo is settling down, let’s try to set the record straight. The report investigated and established the failure of the Numeracy Project by:

providing evidence of a decline in student maths performance that aligns with the roll-out of the Project;

debunking the myth that it’s not such a bad thing that Kiwi kids don’t “know” anything anymore because their strength lies in the higher-order areas of “applying” and “reasoning”, unlike their east-Asian rote-learning counterparts. Sorry, but it turns out those east-Asian kids are not only better at “knowing”, they’re also better at “applying” and “reasoning” because they’ve actually got some knowledge to work with.

The report also investigated maths teaching quality in our primary schools, citing a study in which a significant proportion of 125 student teachers were unable to answer some basic primary-level maths questions. Personally, I feel this raises some serious questions about the quality of the Bachelor of Education degree. Is it not reasonable to expect that all graduating primary school teachers should be able to do primary school maths?

Critics called it unfair, but Rose Patterson was professionally compelled to examine teacher quality after interviewing curriculum writer Vince Wright and maths education researcher Jenny Young-Loveridge. Both interviewees prefer to blame the failure of the Numeracy Project on its poor implementation by teachers rather than its flawed ideology. It really wasn’t the Herald’s finest moment when it accused the report, and by association the Minister of Education because she agreed to launch the report, of criticising teachers. Not one single journalist mentioned the report’s actual conclusion: that teacher quality was unlikely to have changed over the past 15 years, and that the decline in student maths performance was due to the Numeracy Project’s multiple strategy approach to numeracy and the loss of emphasis on the basics.

I am pleased that I had the opportunity to speak publicly in support of our teaching workforce. Frankly, it is shameful that the people who are supposed to be looking after our teachers chose to not defend them. Instead, the NZEI Te Riu Roa president said underfunding for teacher professional development (PD) was to blame for the poor results, even though the report pointed out that New Zealand spends a lot of money on maths PD – more than most other countries, in fact. Even after the Minister of Education responded to the “maths problem” by promising to raise the quality of maths teaching through more PD, the NZEI president still wasn’t happy, saying things would only improve if the training was better than what’s currently available.

Sigh. Result. By the way, has anybody thought about the children lately? When political and professional pride get in the way of helping our kids, it is really sad.

Had certain things happened or not happened, the political response to the Un(ac)countable report might have panned out quite differently. But, having been to Wellington and heard with my own ears the Minister of Education’s response, it is clear there is more work to be done. Nobody could have held the Minister accountable for the mistakes of past governments. In her own words, the Numeracy Project “was in line with international thinking at the time”, so she missed a great opportunity to renounce it and become the public hero. Instead, everything’s gonna be alright now that we’ve got National Standards. Erm, would these be the same National Standards that her Ministry just deemed as lacking dependability?

I am proud of this campaign’s role in bringing the debate to this point, but merely talking about it won’t help our children. A shocking amount of taxpayers’ money has been spent on what can only be described as a failed experiment. By allowing it to continue, we are failing our children. From here on, we are all accountable.

With respect, the Crown’s recently released National Monitoring Study of Student Achievement has NOT shown that the system is failing a minority of students. To quote: “The curriculum expectation at Year 8 is that students will be working solidly at Level 4. About 41 percent of [approximately 2000] Year 8 students achieved at Level 4 or higher on the KAMSI assessment.” In actual fact, the system is failing the majority of primary school students in New Zealand, not a minority.

It is incorrect to suggest that the Un(ac)countable report continues the age-old debate in education between those who believe in rote learning and those who place a higher value on critical thinking. By doing so, you have precisely proved the report correct: “Rather than striking a good balance between instrumental learning and relational learning, and enabling the two to build on each other, they tend to be falsely dichotomised. They should work in tandem.”

Looking at the graphs, we can see that Year 5 student performance in TIMSS has been on the decline since 2002, Year 9 student performance in TIMSS has also been on the decline since 2002, and PISA 2012 showed a sharp decline in the performance of 15-year-old students in mathematical literacy, in stark contrast to the OECD average. To say that New Zealand student performance in these international assessments has “declined slightly in recent years” is something of an understatement.

Your commitment to raise the quality of maths teaching in New Zealand is welcome. However, the Un(ac)countable report shows that teacher quality is unlikely to have changed over the last 15 years, and the true reason for the decline in New Zealand student performance in mathematics is the loss of emphasis on the basics. Until the Ministry acknowledges the overwhelming evidence and addresses the deficiencies in curriculum content and delivery, throwing more money at professional development for teachers will, sadly, have little effect. That is why I have decided to share this letter, so that parents, teachers and principals can also examine the evidence and make appropriate choices for the children in front of them. By working together, I am confident that we will bring back column addition to New Zealand’s early primary maths curriculum.

“As an (old) ex teacher I absolutely applaud your appearance and comments on Breakfast TV this morning. You were better than excellent and I couldn’t agree more with EVERYTHING you said.” – G Blackwell

“For me, the most encouraging aspect you shared was that it is possible to turn things around quite quickly, even after all the years that have been wasted trying to teach maths using a method that clearly doesn’t work and also disadvantaged the students. In other words, because you were so very specific about what needed to change and how, you brought a sense of hope, not only to the students who may have been listening to the interview, but to the parents who have felt anguish seeing their children robbed in their mathematical education and knowing this would negatively impact their futures. Thank you Audrey.” – S Maxwell

Pardon the cynicism, but why on earth would the Ministry of Education release a report late on a Friday before a long weekend, if not to bury bad news?

The National Monitoring Study of Student Achievement 2013 found that only 41 percent of [approximately 2000] Year 8 students achieved at Level 4 or higher on the KAMSI assessment. The curriculum expectation at Year 8 is that students will be working solidly at Level 4.

It is hardly any wonder that older primary school children are failing to grasp maths fundamentals such as fractions and decimals. Too many of them are still muddling their way through the list of whole number strategies, such as “doubling and having”, “tripling and thirding”. Assuming they have already learned how to perform column-based multiplication (which many of them haven’t), their time would be better spent experiencing decimals, fractions and percentages in a variety of ways. And I don’t mean colouring in pictures of fractions; I mean learning how to actually do maths with these numbers.

Readers will be pleased to know that we already have a name for “space and shape” mathematics. It’s called geometry.

I put it to the Ministry of Education that students’ lack of exposure to “formal maths” is a direct consequence of students’ over-exposure to numeracy strategies. There are only so many hours in a school day, after all.

But let’s remain optimistic. The Ministry may never admit that the Numeracy Project was an abject failure, but the report paves the way for them to quietly sweep it under the carpet. The term “formal maths” suggests more direct teaching and less discovery-based learning.

“Too many education reforms are failing to measure success or failure in the classroom,” said Dr Andreas Schleicher. He is right, but in 2009, New Zealand’s National Education Monitoring Project (NEMP) concluded that “…over the 12 years from 1997 to 2009 there has been a small net improvement in mathematics performance at year 4 level (held back from a larger improvement by the decline between 2001 and 2005 in basic fact knowledge), and essentially no net change in mathematics performance at year 8 level.”

So we did have an effective evaluation in place. What happened next? NEMP got shut down and the new curriculum remains intact. It really is time for parents and teachers to demand something better from the Ministry of Education.